Physics · Units And Measurements · NEET
No. The principle of homogeneity does not allow it. You can only add or subtract quantities that have the same dimensions, for example length + length or velocity - velocity. In s = ut + (1/2)at^2, every term (s, ut, and (1/2)at^2) has the dimension of length [L], so the equation is valid. If any term had a different dimension, the equation would be wrong.
No, and this is a common trap. Homogeneity only checks that dimensions match. It cannot catch a wrong number in front, like writing s = 2ut + at^2 instead of s = ut + (1/2)at^2 - both are dimensionally correct because pure numbers have no dimensions. So dimensionally correct is necessary but not sufficient. For NEET, remember: homogeneity can prove an equation wrong, but it cannot prove it fully right.
They are all dimensionless. The angle inside sin, cos, or tan must be a pure number (dimensionless), so whatever you put inside the bracket, such as (kx - wt), must itself be dimensionless. Same for the power in e^x and the input of a logarithm. By homogeneity, if you see sin(kx), then kx has no dimension, which lets you quickly find the dimension of k.
For checking dimensions, no. Pure numbers like 2, 1/2, or pi have zero dimensions [M^0 L^0 T^0], so they do not change the dimension of a term. That is exactly why homogeneity cannot detect a wrong numerical factor. But a dimensional constant (like G or a spring constant) does carry dimensions and must be included.
Because an equation says two things are equal, and you can only equate quantities of the same kind. If the left side is a length and the right side is a time, the statement is meaningless, like saying 5 metres = 3 seconds. So the = sign obeys homogeneity just like the + and - signs do.
A force defined by F = alpha t + beta t^2 acts on a particle at a given time t. If alpha and beta are constants, the factor which is dimensionless is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It says that in a correct physical equation, each term joined by +, -, or = must have exactly the same dimensions. You cannot mix different kinds of quantities in the same equation.
First, to check whether a given equation is dimensionally correct (consistency check). Second, to find the dimension of an unknown quantity or constant by matching it with the other terms, for example finding the dimension of a constant inside sin or e^x.
Because pure numbers and constants like 1/2, 2, or pi have no dimensions. So a formula with a wrong numerical factor can still pass the dimension check. Homogeneity can only reject wrong equations, not fully confirm right ones.
Yes. Angles, and the inputs of sin, cos, tan, log, and e^x, are all dimensionless. So any expression inside these functions must be a pure number, which helps you find unknown dimensions using homogeneity.
